• School Mathematics
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• v.7 no.2
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• pp.123-137
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• 2005

Elementary combinatorial problem may be classified into three different combinatorial models(selection, distribution, partition). The main goal of this research is to determine the effect of type of combinatorial operation and implicit combinatorial model on problem difficulty. We also classified errors in the understanding combinatorial problem into error of order, repetition, permutation with repetition, confusing the type of object and cell, partition. The analysis of variance of answers from 339 students showed the influence of the implicit combinatorial model and types of combinatorial operations. As a result of clinical interviews, we particularly noticed that some students were not able to transfer the definition of combinatorial operation when changing the problem to a different combinatorial model. Moreover, we have analysed textbooks, and we have found that the exercises in these textbooks don't have various types of problems. Therefore when organizing the teaching , it is necessary to pose various types of problems and to emphasize the transition of combinatorial problem into the different models.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2001.11a
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• pp.166-171
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• 2001

In order to improve the efficiency of the design process and the quality of the resulting design for the application-based exclusive rolling element bearings, this study propose design methodologies by using a genetic-based combinatorial optimization. By the presence of discrete variables such as the number of rolling element (standard component) and by the engineering point of views, the design problem of the rolling element bearing can be characterized by the combinatorial optimization problem as a fully discrete optimization. A genetic algorithm is used to efficiently find a set of the optimum discrete design values from the pre-defined variable sets. To effectively deal with the design constraints and the multi-objective problem, a ranking penalty method is suggested for constructing a fitness function in the genetic-based combinatorial optimization. To evaluate the proposed design method, a robust performance analyzer of ball bearing based on quasi-static analysis is developed and the computer program is applied to some design problems, 1) maximize fatigue life, 2) maximize stiffness, 3) maximize fatigue life and stiffness, of a angular contact ball bearing. Optimum design results are demonstrate the effectiveness of the design method suggested in this study. It believed that the proposed methodologies can be effectively applied to other multi-objective discrete optimization problems.

• Applied Chemistry for Engineering
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• v.21 no.4
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• pp.357-365
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• 2010

Combinatorial synthesis, which has been adopted as an efficient method for deriving a leading compound in pharmaceutical chemistry, is recently being applied in various fields along with the rapid development of analysis and examination technology. It is especially attracting much attention as an efficient strategy to secure various potent compounds rapidly in the areas of developing new materials where the relationship between the chemical structure and the property is not revealed. Several reports and reviews have already been published for the combinatorial chemistry and combinatorial synthesis. This report briefly introduces trends in the combinatorial development of new materials and discusses the cases of developing organic luminescent materials.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.675-681
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• 2018

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify three families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind and establish a new family of nonlinear ordinary differential equations in terms of the Stirling numbers of the second kind.

• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.295-311
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• 2016

This paper addresses to the flowshop scheduling problem with blocking constraints. The objective is to minimize the makespan criterion. We propose a hybrid combinatorial particle swarm optimization algorithm (HCPSO) as a resolution technique for solving this problem. At the initialization, different priority rules are exploited. Experimental study and statistical analysis were performed to select the most adapted one for this problem. Then, the swarm behavior is tested for solving a combinatorial optimization problem such as a sequencing problem under constraints. Finally, an iterated local search algorithm based on probabilistic perturbation is sequentially introduced to the particle swarm optimization algorithm for improving the quality of solution. The computational results show that our approach is able to improve several best known solutions of the literature. In fact, 76 solutions among 120 were improved. Moreover, HCPSO outperforms the compared methods in terms of quality of solutions in short time requirements. Also, the performance of the proposed approach is evaluated according to a real-world industrial problem.

• Proceedings of the Polymer Society of Korea Conference
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• 2006.10a
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• pp.110-111
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• 2006

Most applications of polymers involve blends and mixtures of components including solvents, surfactants, copolymers, fillers, organic or inorganic functional additives, and various processing aids. These components provide unique properties of polymeric materials even beyond those tailored into the basic chemical structures. In addition, skillful processing extends the properties for even greater applications. The perennial challenge of polymer science is to understand and exploit the structure-processing-property interplay relationship. We are developing and demonstrating combinatorial methods and high throughput analysis as tools to provide this fundamental understanding.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.1
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• pp.27-36
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• 2000

We perform a computational complexity analysis of a heuristic algotithm proposed in the literature for the combinatorial optimization problems extended with a single side-constraint. This algorithm, although such a view was not given in the original work, is a disguised version of an optimal Lagrangian dual solution technique. It also has been observed to be a very efficient heuristic producing near-optimal solutions for the primal problems in some experiments. Especially, the number of iterations grows sublinearly in terms of the network node size so that the heuristic seems to be particularly suitable for the applicatons such as routing with semi-real time requirements. The goal of this paper is to establish a polynomal worst-case complexity of the algorithm. In particular, the obtained complexity bound suports the sublinear growth of the required iterations.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1999.10a
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• pp.172-172
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• 1999

• Journal of Powder Materials
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• v.23 no.2
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• pp.143-148
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• 2016

A microfluidic reactor with computer-controlled programmable isocratic pumps and online detectors is employed as a combinatorial synthesis system to synthesize and analyze materials for fabricating CdSe quantum dots for various applications. Four reaction condition parameters, namely, the reaction temperature, reaction time, Cd/Se compositional ratio, and precursor concentration, are combined in synthesis condition sets, and the size of the synthesized CdSe quantum dots is determined for each condition. The average time corresponding to each reaction condition for obtaining the ultraviolet-visible absorbance and photoluminescence spectra is approximately 10 min. Using the data from the combinatorial synthesis system, the effects of the reaction conditions on the synthesized CdSe quantum dots are determined. Further, the data is used to determine the relationships between the reaction conditions and the CdSe particle size. This method should aid in determining and selecting the optimal conditions for synthesizing nanoparticles for diverse applications.

• Journal of Computing Science and Engineering
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• v.8 no.4
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• pp.199-206
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• 2014

The ant colony optimization (ACO) algorithm is a new heuristic algorithm that offers good robustness and searching ability. With in-depth exploration, the ACO algorithm exhibits slow convergence speed, and yields local optimization solutions. Based on analysis of the ACO algorithm and the genetic algorithm, we propose a novel hybrid genetic ant colony optimization (NHGAO) algorithm that integrates multi-population strategy, collaborative strategy, genetic strategy, and ant colony strategy, to avoid the premature phenomenon, dynamically balance the global search ability and local search ability, and accelerate the convergence speed. We select the traveling salesman problem to demonstrate the validity and feasibility of the NHGAO algorithm for solving complex optimization problems. The simulation experiment results show that the proposed NHGAO algorithm can obtain the global optimal solution, achieve self-adaptive control parameters, and avoid the phenomena of stagnation and prematurity.